I assumed you are a stay at home mum since money is an issue and your husband questioned you if you have money to go out. It's not easy supporting a family and your husband could be drained from working and need ME time by being alone. Of course, extended periods of isolated time is not healthy and the wife and kids feels neglected too.
You are not alone about the sex part too. Ever since I give birth my husband is also used to giving direct sex, no hugging, kissing, arousing like you mentioned. I am always straightforward abt my needs to him but end up we rarely did full set foreplay as well. Not sure is it because we are older, more tired or lack of time... I do missed the times when we are in a more relaxed mood to have sex before baby comes.
For outings, there are plenty of free places to enjoy with the kids. There are so many museums that are free of entry, not forgetting public parks where kids can burn off their energy and you can picnic as well. Even if no picnic, there are options like going to Mac nearby or the nearest shopping centre for foodcourt meal. Do not think that kids must go SEA Aquarium or Kids zania or USS. Thats is obviously expensive in the long run...
Just to share these couple of days, my husband off from work and we went to Datoka crescent to explore since it's going to be gone. Bring then to explore for old neighbourhood feel and the classic old playground with tire swings. Today we also went for swimming using ActiveSG credit and we had some fun too. These trips are FOC neverthless and we also settle for hawker food and coffee shop food.
No recommendations for counselling but great that both of you are willing to work this out :)