This is my best assessment for your situation regarding to the marriage place and form, and the baptism of children of a man and a woman that are both baptised but only one is Catholic.
Assuming you are not in danger of death and not in a place without access to priests for a more than a month, then for the marriage to be valid (this is, for the church to say that you have actually married) you would need a special permission from the Bishop (called dispensation). This is because Catholics are not expected prima face to marry non-Catholics.
Normally you would not need to talk to the Bishop, usually the priest has a form that once filled it means that that permission is granted. For the Bishop to grant permission at least three requirements are needed
A) the Catholic party has to a) declare that he or she is prepared to remove dangers of defecting from the faith, and b) make a sincere promise to do all in his or her power so that all offspring are baptized and brought up in the Catholic Church. (CIC 1125.1)
B) The non-catholic party does not need to promise anything regarding the upbringing of the children (as it had to do in the past), but has to declare that he or she is aware of the promise that the Catholic party is making. (CIC 1125.2)
C) Finally all the parties have to be aware of the nature of marriage as a covenant of a man and a women for the purpose to establish a partnership for the whole life, with the purpose of the wellbeing of the partner and the procreation and upbringing of children. None of these can be excluded from each of the marrying parties.
If A+B+C are fulfilled, normally by signing on a form at the parish days before the marriage, then the permission almost certainly granted to marry *under the same conditions of the rest of the Catholics (ex, you cannot marry a person who is already married).
Now, the conditions that in normal circumstances two Catholics need to abide for a valid marriage include the place and the type of ceremony of the marriage, called a canonical form. The place should be a Catholic parish and the form a Nuptial Mass (with communion) or wedding service. Since the non-Catholic party cannot take communion in the Catholic Church usually the wedding is done without a mass in a wedding service inside the church. In this case, the assistant of the wedding (the person who ask for the consent of the parties and receives it in the name of the Church) needs to be a Catholic priest or a deacon, two witnesses are required who don't need to be Catholic, and during the ceremony a non-Catholic person can speak to the parties and bless them.
Now, if you want another form for the marriage, say a) a different place than a Catholic church, or a different kind of of ceremony (say Orthodox or Lutheran format) you would need to ask another permission (dispensation of the canonical form) from the Bishop. In most or maybe all dioceses this is not commonly granted and you would possible need to write the Bishop through the local priest to ask for a dispensation for pastoral reasons (maybe family tensions). It is possible that the place could be changed, and maybe even some sort of ceremony style, but it is far less likely and a very very rare exception (but still possible) that someone not Catholic would be allowed to assist (ask for the vows). If you want to go to the latter line I would recommend to ask help from a pastoral advisor and a cannon lawyer, as well as to your local the priest, as these are complicated matters.
Now, you have to know also that the Church forbids to have two wedding ceremonies or a ceremony with two wedding rituals. Since the Catholic party is not required to promise not to have another ceremony, you would still be in a valid marriage if you were to keep secret plans to marry afterwards in another denomination, and do it after your Catholic marriage. The marriage would be valid if the A+B+C conditions are fulfilled, yet at the same time the Catholic party could possibly be forfeiting the good standing with the Catholic Church by formally and publicly acting against her rules.
Now, about the baptism. For a baptism to be valid (this is, recognised by the Church, who would not do another one) the only conditions are a) that water is used b) that the trinitarian words "I baptise you in the name of the Father, and of the Son, and of the Holy Spirit" are used c)
that the baptism is made with the intention to baptise (as opposed to theatre etc). This conditions are fulfilled by almost all protestant denominations and this is why the Catholic Church does not re-baptise converts from the Luteran Church or Anglican Church for instance.
Now for baptism to be licit (this is according to the rules) then more conditions have to be fulfilled. For infants, it is required that there is a Catholic sponsor, that at least one parent or people (or legal equivalent) intends the child to be brought up as Catholic. Baptisms are also to be performed in the Church, by a priest or deacon. Now, again, except in the case of near death when rules don't matter, one can ask the Bishop, through a priest, for a dispensation of the these rules. I know that inter-denominational families in England had managed to get the baptisms that are as being in accordance with Catholic and Church of England denominations. In this way the child gets registered in both churches documents. If, without asking for a dispensation, the rules are not followed, but the conditions a)+b)+c) are still fulfilled then the child does not get registered in the documents of the Catholic parish, but the Catholic church recognises that the child has been baptised and will not re-baptise it again. To get the first communion or confirmation in the Catholic Church, since it is required to be a Catholic, some sort of small ceremony would be needed. Usually this would consist in a welcome-into-our-parish announcement by the priest in a particular mass where the child is to be present.
All in all. For the marriage, the easiest way to go is to get a marriage in the Catholic parish with a Catholic priest asking for the consent, but allowing (by negotiating in advance) for the speech and blessing to be done by someone from the other denomination. As for the Baptism, the easiest thing is to get the child baptised as all other catholics but there are two other options. The firs option is to ask the Bishop's permission for the baptism to be done somewhere else or by a non-catholic person. Some Bishops agree to this (I think) when they see a strong commitment that the child even if baptised somewhere else would be brought up Catholic. Notice that the catholic party in the marriage has promised to to all in his or her power to rise the children Catholic, but since God doesn't ask the impossible if the marriage is in danger this obligation is suppressed. There are reluctant bishops known to have changed their minds once the child kept being un-baptised for months because of family tensions, and agree better give a dispensation and get it baptised. The third would route to disregard church rules and baptise the child anyway, in which case if a)+b)+c) are followed the baptism is ilicit but still valid. I don't see a need for this. Usually one can convince the bishop, and if the family tensions are great, one can keep talking to the bishop until he agrees.